Question: Solve for $x$ and $y$ by deriving an expression for $x$ from the second equation, and substituting it back into the first equation. $\begin{align*}-5x-4y &= 7 \\ -2x-4y &= 1\end{align*}$
Solution: Begin by moving the $y$ -term in the second equation to the right side of the equation. $-2x = 4y+1$ Divide both sides by $-2$ to isolate $x$ $x = {-2y - \dfrac{1}{2}}$ Substitute this expression for $x$ in the first equation. $-5({-2y - \dfrac{1}{2}}) - 4y = 7$ $10y + \dfrac{5}{2} - 4y = 7$ Simplify by combining terms, then solve for $y$ $6y + \dfrac{5}{2} = 7$ $6y = \dfrac{9}{2}$ $y = \dfrac{3}{4}$ Substitute $\dfrac{3}{4}$ for $y$ in the top equation. $-5x-4( \dfrac{3}{4}) = 7$ $-5x-3 = 7$ $-5x = 10$ $x = -2$ The solution is $\enspace x = -2, \enspace y = \dfrac{3}{4}$.